Photonic systems provide a variety of different physical representations for quantum information. One type of physical representation uses the polarization of photons to encode quantum information. In particular, each photon has a polarization state that can be expressed as a linear combination of two basis states associated with orthogonal polarizations (e.g., horizontal and vertical polarization states |H> and |V> or right and left circularly polarized states |R> and |L>). A quantum information processing system can use the two orthogonal polarization states of a photon as the basis state values |0> and |1> of a qubit. In some alternative physical representations, a qubit has basis state values |0> and |1> corresponding to orthogonal eigen states of orbital angular momentum of a photon, the presence or the absence of a photon in a single spatial channel or time bin, or to the alternative presence of a single photon in one or the other of two spatial channels or in one or the other of two time bins.
More generally, quantum information is not limited to qubits. A qudit, for example, refers to quantum information represented using d discrete basis states, and a qunat refers to quantum information represented using a continuous range of basis states. One photonic representation of a qudit uses the alternative presence of a single photon in any one of d distinct spatial channels or of d distinct time bins. Alternatively, the Fock states (e.g., states |0> to |d−1>) containing definite numbers (e.g., 0 to d−1) of photons can be the basis states for encoding qudit having any desired number d of discrete values, and the orbital angular momentum of states containing one or more photons can similarly represent three or more discrete values of a qudit. Similarly, a qunat can be physically represented using photons having a continuous range of eigen values for an operator such as position or momentum or approximately represented using coherent or squeezed photon states |α> corresponding to a continuous quantum variable α. Many other representations of quantum information such as qubits, qudits, and qunats are possible using photonic systems. The entanglement of photon states is another general form of quantum information that can be physically represented using many types of photon states.
Quantum information processing generally manipulates quantum states to perform tasks such as calculations or communications, storage, or measurement of quantum information. For example, a system that manipulates quantum states can implement a variety of logical operations that are often associated with the quantum gates. However, an implementation of one quantum gate may be more efficient for one physical representation of quantum information, while another quantum gate is more difficult to implement for that physical representation. More specifically, a first quantum gate for a qubit, for example, may be most easily implemented if the qubit is represented with photons of one frequency, but a second quantum gate may be more efficiently implemented if the qubit is represented using photons having a different frequency. Specific implementations of systems that store or measure quantum information may similarly be most efficient or easiest to implement for a specific physical representation of the quantum information. Accordingly, the choice of a fixed physical representation (e.g., of the frequency and the encoding of photons used to represent the quantum information) may limit the availability or efficiency of a quantum information processing system.